THEORY OF OPTICAL-PHONON LIMITED HOT-ELECTRON TRANSPORT IN QUANTUM WIRES

We present a kinetic theory of a nonequilibrium electron gas in a one- dimensional circular quantum wire interacting with acoustic and polar optical phonons. Besides these scattering mechanisms we also include a n elastic interaction with interface roughness for the electron moment um relaxation. We have solved the Boltzmann kinetic equation analytica lly and obtained different distribution functions for a one-dimensiona l electron gas. A detailed kinetic analysis of the limiting case of th e electron gas interacting solely with optical phonons is undertaken a nd the distribution function is found when this system can be describe d in a self-consistent way. Our analytical results are in good agreeme nt with previous numerical studies of a similar system using Monte Car lo techniques. As an application of the developed theory we have calcu lated the electric-field dependences of electron mobility and average energy for different parameters of the quantum wire. It is shown that at high lattice temperature the electron mobility is a nonmonotonous f unction of the applied electric field and has its maximum value at int ermediate electric fields when the transition from acoustic-phonon-lim ited to optical-phonon-limited transport takes place.